<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-03-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001348259</issuerCik>
        <issuerName>VALIDUS HOLDINGS LTD</issuerName>
        <issuerTradingSymbol>VR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001407196</rptOwnerCik>
            <rptOwnerName>Singh Alok</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VALIDUS RE</rptOwnerStreet1>
            <rptOwnerStreet2>48 PAR-LA-VILLE ROAD, SUITE 1790</rptOwnerStreet2>
            <rptOwnerCity>HAMILTON</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM11</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Note (4) Below</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>716031.48</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2007-09-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-12-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>716031.48</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>55392.07</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2007-09-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-12-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>55392.07</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12632.01</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2007-09-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-12-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12632.01</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The securities sold were directly owned by New Mountain Partners II (Cayman), L.P.</footnote>
        <footnote id="F2">The securities sold were directly owned by Allegheny New Mountain Partners (Cayman), L.P.</footnote>
        <footnote id="F3">The securities sold were directly owned by New Mountain Affiliated Investors II (Cayman), L.P.</footnote>
        <footnote id="F4">NMI II (Cayman) GP, Ltd. is the general partner of New Mountain Investments II (Cayman), L.P., which is the general partner of each of New Mountain Partners II (Cayman), L.P., Allegheny New Mountain Partners (Cayman), L.P. and New Mountain Affiliated Investors II (Cayman), L.P. (collectively, the &quot;New Mountain Funds&quot;).  Alok Singh is a managing director of New Mountain Capital, L.L.C.  Mr. Singh disclaims beneficial ownership of the common stock warrants owned by the New Mountain Funds, except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Alok Singh</signatureName>
        <signatureDate>2013-03-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
